Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911585352548352 |
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| author | Crépey, Stéphane Frikha, Noufel Louzi, Azar Pagès, Gilles |
| author_facet | Crépey, Stéphane Frikha, Noufel Louzi, Azar Pagès, Gilles |
| contents | Crépey, Frikha, and Louzi (2025) introduced a nested stochastic approximation algorithm and its multilevel acceleration to compute the value-at-risk and expected shortfall of a random financial loss. We hereby establish central limit theorems for the renormalized estimation errors associated with both algorithms as well as their averaged versions. Our findings are substantiated through a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15333 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall Crépey, Stéphane Frikha, Noufel Louzi, Azar Pagès, Gilles Risk Management Probability Computational Finance 65C05, 62L20, 62G32, 91Gxx Crépey, Frikha, and Louzi (2025) introduced a nested stochastic approximation algorithm and its multilevel acceleration to compute the value-at-risk and expected shortfall of a random financial loss. We hereby establish central limit theorems for the renormalized estimation errors associated with both algorithms as well as their averaged versions. Our findings are substantiated through a numerical example. |
| title | Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall |
| topic | Risk Management Probability Computational Finance 65C05, 62L20, 62G32, 91Gxx |
| url | https://arxiv.org/abs/2311.15333 |